Definitely two syllables, similar to Wooster (Ohio?). Or, if you should happen to come from around here, "WOO-stah". (That's "oo" as in "foot".) The sauce is "woo-ster-shear" sauce, from the place in England. It's the ineffable British condensation, which also makes Leicester be pronounced "Lester" and Leominster "Leminster" and, inevitably, turns Cholmondeley into "Chumley". (And reaches its epitome when it renders eleemosynary as "alms," by now a fait accompli.)

But all those are shortenings. Why _add_ a letter/change the phoneme? If it were just the literal mind operating it should have come out wor-ses-ter, not -chester.